• International Journal of CAD/CAM
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• v.7 no.1
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• pp.91-101
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• 2007

To understand the structure of molecules, various computational methodologies have been extensively investigated such as the Voronoi diagram of the centers of atoms in molecule and the power diagram for the weighted points where the weights are related to the radii of the atoms. For a more improved efficiency, constructs like an $\alpha$-shape or a weighted $\alpha$-shape have been developed and used frequently in a systematic analysis of the morphology of molecules. However, it has been recently shown that $\alpha$-shapes and weighted $\alpha$-shapes lack the fidelity to Euclidean distance for molecules with polysized spherical atoms. We present the theory as well as algorithms of $\beta$-shape and $\beta$-complex in $\mathbb{R}^3$ which reflects the size difference among atoms in their full Euclidean metric. We show that these new concepts are more natural for most applications and therefore will have a significant impact on applications based on particles, in particular in molecular biology. The theory will be equivalently useful for other application areas such as computer graphics, geometric modeling, chemistry, physics, and material science.

• Journal of Information Processing Systems
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• v.16 no.2
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• pp.406-420
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• 2020

In order to make up the deficiencies of the existing research results which cannot effectively deal with the nearest neighbor query based on the line segments in obstacle space, the k nearest neighbor query method of line segment in obstacle space is proposed and the STA_OLkNN algorithm under the circumstance of static obstacle data set is put forward. The query process is divided into two stages, including the filtering process and refining process. In the filtration process, according to the properties of the line segment Voronoi diagram, the corresponding pruning rules are proposed and the filtering algorithm is presented. In the refining process, according to the relationship of the position between the line segments, the corresponding distance expression method is put forward and the final result is obtained by comparing the distance. Theoretical research and experimental results show that the proposed algorithm can effectively deal with the problem of k nearest neighbor query of the line segment in the obstacle environment.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.4 no.2
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• pp.193-198
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• 2004

This paper describes an automatic finite element (FE) mesh generation for three-dimensional structures consisting of tree-form surfaces. This mesh generation process consists of three subprocesses: (a) definition of geometric model, (b) generation of nodes, and (c) generation of elements. One of commercial solid modelers is employed for three-dimensional solid structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Voronoi diagram method is introduced as a basic tool for element generation. Automatic generation of FE meshes for three-dimensional solid structures holds great benefits for analyses. Practical performances of the present system are demonstrated through several mesh generations for three-dimensional complex geometry.

• Korean Journal of Computational Design and Engineering
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• v.12 no.6
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• pp.422-428
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• 2007

Presented in the paper is a procedure to reconstruct a triangular mesh from a point cloud. Although, the proposed procedure is based on the well-known Voronoi diagram approach, it introduces a selection method of 'Pole' to improve the quality of resulting mesh. To select the appropriate Poles for high quality of Triangular mesh, the patterns that the Poles affect to the mesh quality are carefully analyzed. It is possible to improve the mesh quality by controlling the selection method of 'Pole' in terms of distance limit. The initial mesh obtained by the proposed procedure may include invalid triangles. To relieve this problem, a slicing method is proposed to remove invalid triangles from the initial mesh. At last, correcting technique of normal vectors of generated mesh is introduced.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.12
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• pp.6986-6992
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• 2014

The generalized Voronoi graph (GVG) is a topological map of a constrained environment. This is defined in terms of workspace distance measurements using only sensor-provided information, with a robot having a maximum distance from obstacles, and is the optimum for exploration and obstacle avoidance. This is the safest path for the robot, and is very significant when studying the GVG edges of highly articulated robots. In previous work, the point-GVG edge and Rod-GVG were built with point robot and rod robot using sensor-based control. An attempt was made to use a higher degree of freedom robot to build GVG edges. This paper presents GVG-based a new local roadmap for the two-link robot in the constrained two-dimensional environment. This new local roadmap is called the two-identical-link generalized Voronoi graph (L2-GVG). This is used to explore an unknown planar workspace and build a local roadmap in an unknown configuration space $R^2{\times}T^2$ for a planar two-identical-link robot. The two-identical-link GVG also can be constructed using only sensor-provided information. These results show the more complex properties of two-link-GVG, which are very different from point-GVG and rod-GVG. Furthermore, this approach draws on the experience of other highly articulated robots.

• Proceedings of the IEEK Conference
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• 2003.07a
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• pp.89-92
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• 2003

A geometrically uniform code in AWGN channel has strong symmetry properties such as a) the distance profiles form codewords On C to all other codewords are all the same, and b) all Voronoi regions of codewords in C have the same shape. Such properties make the word error probability of geometrically uniform codes be transparent to the transmitted codeword. In this paper, we extend the geometrically uniform codes in AWGN channel to the geometrical uniform codes in fading channel with multiple transmit antennas.

• Journal of Cadastre & Land InformatiX
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• v.48 no.2
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• pp.185-195
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• 2018

In the Seoul Metropolitan City, the PM(pariculate matter) application used by the citizens provides the PM concentration of the nearest monitoring stations located on the PM monitoring stations. Currently, the selecting method of the PM monitoring network considered by the Ministry of Environment is based on considering the monitoring station distribution and population density only. In this study, we analyzed the distance between PM monitoring station and the administrative center point in addition to the above considerations. The number of test sites was verified and the range of coverage of each monitoring stations was indicated by using the Voronoi algorithm and hexagon grid. The spatial position problem of the PM monitoring station was suggested by spatial data analysis. The variables of spatial data analysis are single-family houses, apartments, $1^{st}$ class neighborhood, $2^{nd}$ class neighborhood, garbage disposal plant, hazardous material disposal facility, factory, and the density map. The analysis result of the selection criterion considering the additional variables for new PM monitoring stations was presented, in addition to the selection criteria provided by the Ministry of Environment.

• Journal of the Korean Society of Marine Environment & Safety
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• v.23 no.7
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• pp.775-782
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• 2017

The position of existing patrol ships has been decided according to subjective judgments, not purely by any reasonable or scientific criteria, because of a lack of access to marine accident positions. In this study, the optimal location of patrol ships is quantitatively determined based on historical marine accident data. The study area used included the coastal sea of Pohang in South Korea. In this study, a k-means clustering algorithm was used to derive the location of patrol ships, and then a Voronoi diagram was used to divide the region around each patrol ship. As a result, the average navigation distance for patrol ships was improved by 4.4 nautical miles, and the average arrival time was improved by 13.2 minutes per marine accident. Moreover, if the locations of patrol ships need to be changed flexibly, it will be possible to optimally arrange limited resources using the technique developed in this study to ensure a fast rescue.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.8
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• pp.385-393
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• 2008

The best coverage problem is finding a path whose worst distance to the sensor-set is the best among all paths. Instead, if the user stays close to its nearest two sensors, then the stability of the wireless connection may be guaranteed. So we consider the problem of finding a second best coverage path; given the sensor set U, a starting point s and a target point t, find a path whose worst distance to the second closest sensor is minimized. This paper presents an O(n logn) -time algorithm to find such a path. We also give experimental evidence showing that the connection to the sensor-set along a second best coverage path is more stable than that along the best coverage path.

• Journal of Korea Multimedia Society
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• v.9 no.2
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• pp.139-150
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• 2006

A schematic map is a special purpose map which is generated to recognize it's objects easily and conveniently via simplifying and highlighting logical geometric information of a map. To manufacture the schematic map with road, label and icon, we must generate simplified route map and replace many geometric objects. Performing a give task, however, there are an amount of overlap areas between geometric objects whenever we process the replacement of geometry objects. Therefore we need replacing geometric objects without overlap. But this work requires much computational resources, because of the high complexity of the original geometry map. We propose the schematic map generation system whose map consists of icons and label. The proposed system has following steps: 1) eliminating kinks that are least relevant to the shape of polygonal curve using DCE(Discrete Curve Evolution) method. 2) making an evenly distributed route using CVT(Centroidal Voronoi Tessellation) and Grid snapping method. Therefore we can keep the structural information of the route map from CVT method. 3) replacing an icon and label information with collision avoidance algorithm. As a result, we can replace the vertices with a uniform distance and guarantee the available spaces for the replacement of icons and labels. We can also minimize the overlap between icons and labels and obtain more schematized map.